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		<P class='majorTitle'>com.wis.math.calc.solvers.EulerRichardson Documentation</P>

        <P><B>Author:</B> <a href='mailto:wisolutions2002@shaw.ca?subject=wisASLibrary  EulerRichardson Class'>Richard Wright</a><BR>
		<B>Last Modified:</B> 01/11/05 21:00:14<HR class='big'>

		<P class='sectionTitle'>Summary</P>
		<P class='ToC'>com.wis.math.calc.solvers.EulerRichardson class:</P>
		<div class='methodsDiv'><a href='#classinfo'>- description</a></div>
<P class='ToC'>com.wis.math.calc.solvers.EulerRichardson Properties:</P><div class='methodsDiv'>
<a href='#$stepSize'>- $stepSize</a><br>
<a href='#$numEqn'>- $numEqn</a><br>
<a href='#$rate'>- $rate</a><br>
<a href='#$midstate'>- $midstate</a><br>
<a href='#$ode'>- $ode</a><br>
</div><br>
<P class='ToC'>com.wis.math.calc.solvers.EulerRichardson Methods:</P><div class='methodsDiv'>
<a href='# initialize'>-  initialize</a><br>
<a href='# step'>-  step</a><br>
<a href='# setStepSize'>-  setStepSize</a><br>
<a href='# getStepSize'>-  getStepSize</a><br>
<a href='# setTolerance'>-  setTolerance</a><br>
<a href='# getTolerance'>-  getTolerance</a><br>
</div><br>

		<HR class='big'>
		<P class='sectionTitle'><A name='classinfo'></A>com.wis.math.calc.solvers.EulerRichardson <I>class</I></P>
		<P> <span class='methodTitle'>version:</span> 1.7</P>
		<P class="methodTitle">description:</P>
		<P>EulerRichardson implements the behaviours of the IODESolver Interface
 -- it constructs the EulerRichardson IODESolver for a system of ordinary
 differential equations. The Euler-Richardson method uses the state at
 the beginning of the interval to estimate the state at the midpoint.

 <pre> x(midpoint) = x(n) + v(n)dt/2
 v(midpoint) = v(n) + a(n)dt/2
 t(midpoint) = t(n) + dt/2</pre>

 The midpoint state is then used to calculate the final state.
 </P>
		<P class="methodTitle">usage:</P> <pre>var inst:EulerRichardson = new EulerRichardson(_ode);</pre>

<P> <span class='methodTitle'>parameters:</span>
				<ul>
<li>      _ode  (IODE)  -- the system of differential equations.</li>
</ul>

			<HR class='small'>
			<P class='groupTitle'><A name='properties'></A>com.wis.math.calc.solvers.EulerRichardson Properties:</P>
			<div class='methodsDiv' >


				<P class='methodTitle'><A name='$stepSize'></A><u> $stepSize</u></P>
				<P> (Number)  -- parameter increment such as delta time.</P>

				<P class='methodTitle'><A name='$numEqn'></A><u> $numEqn</u></P>
				<P> (Number)  -- number of equations.</P>

				<P class='methodTitle'><A name='$rate'></A><u> $rate</u></P>
				<P> (Array)  -- array that stores the rate.</P>

				<P class='methodTitle'><A name='$midstate'></A><u> $midstate</u></P>
				<P> (Array)  -- array that stores the midpoint.</P>

				<P class='methodTitle'><A name='$ode'></A><u> $ode</u></P>
				<P> (IODE)  -- object that computes rate.</P>
</div>

			<HR class='small'>
			<P class='groupTitle'><A name='methods'></A>com.wis.math.calc.solvers.EulerRichardson Methods:</P>
			<div class='methodsDiv' >


				<P class='methodTitle'><A name=' initialize'></A><u>  initialize</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Initializes the IODE solver. The rate and midstate arrays are
     allocated. The number of differential equations is determined
     by invoking getState().length on the IODE.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>inst.initialize(_stepSize);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  _stepSize  (Number) -- step integer.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Void)
    </P>

				<P class='methodTitle'><A name=' step'></A><u>  step</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Steps (advances) the differential equations by the stepSize.
     The IODESolver invokes the IODE's getRate method to obtain the
     initial state of the system. The IODESolver then advances the
     solution and copies the new state into the state array at the
     end of the solution step.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>inst.step();</pre>
     </P>
<P><span class='methodAttributesTitle'>returns:</span> (Number)  -- returns step size.
    </P>

				<P class='methodTitle'><A name=' setStepSize'></A><u>  setStepSize</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Sets the step size. The step size remains fixed in
     this algorithm.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>inst.setStepSize(_stepSize);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  _stepSize  (Number) -- step integer.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Void)
    </P>

				<P class='methodTitle'><A name=' getStepSize'></A><u>  getStepSize</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Gets the step size. The stepsize is constant in this algorithm.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>inst.getStepSize();</pre>
     </P>
<P><span class='methodAttributesTitle'>returns:</span> (Number)  -- returns step size
    </P>

				<P class='methodTitle'><A name=' setTolerance'></A><u>  setTolerance</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Abstract interface method.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>not used.</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>  _tol  (Number) -- .</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> (Void)
    </P>

				<P class='methodTitle'><A name=' getTolerance'></A><u>  getTolerance</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Abstract interface method.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>not used.</pre>
     </P>
<P><span class='methodAttributesTitle'>returns:</span> (Number)
    </P>
</div>

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